Funny thing is, I hang around with the horsey set, and they usually wear baseball caps. I guess with a good Resistol, or Stetson running around $200.00 these days (which no real cowboy would wear anything less than), a horse slobbering on a baseball cap is not as big of an issue. These true western horsemen will don their Resistols, or Stetsons on special occasions.
But, guys look so much better in cowboy hats.